Surface Roughness of the Moon Derived from Multi-frequency Radar Data

Surface roughness of the Moon provides important information concerning both significant questions about lunar surface processes and engineering constrains for human outposts and rover trafficabillity. Impact-related phenomena change the morphology and roughness of lunar surface, and therefore surface roughness provides clues to the formation and modification mechanisms of impact craters. Since the Apollo era, lunar surface roughness has been studied using different approaches, such as direct estimation from lunar surface digital topographic relief, and indirect analysis of Earth-based radar echo strengths. Submillimeter scale roughness at Apollo landing sites has been studied by computer stereophotogrammetry analysis of Apollo Lunar Surface Closeup Camera (ALSCC) pictures, whereas roughness at meter to kilometer scale has been studied using laser altimeter data from recent missions. Though these studies shown lunar surface roughness is scale dependent that can be described by fractal statistics, roughness at centimeter scale has not been studied yet. In this study, lunar surface roughnesses at centimeter scale are investigated using Earth-based 70 cm Arecibo radar data and miniature synthetic aperture radar (Mini-SAR) data at S- and X-band (with wavelengths 12.6 cm and 4.12 cm). Both observations and theoretical modeling show that radar echo strengths are mostly dominated by scattering from the surface and shallow buried rocks. Given the different penetration depths of radar waves at these frequencies (< 30 m for 70 cm wavelength, < 3 m at S-band, and < 1 m at X-band), radar echo strengths at S- and X-band will yield surface roughness directly, whereas radar echo at 70-cm will give an upper limit of lunar surface roughness. The integral equation method is used to model radar scattering from the rough lunar surface, and dielectric constant of regolith and surface roughness are two dominate factors. The complex dielectric constant of regolith is first estimated globally using the regolith composition and the relation among the dielectric constant, bulk density, and regolith composition. The statistical properties of lunar surface roughness are described by the root mean square (RMS) height and correlation length, which represent the vertical and horizontal scale of the roughness. The correlation length and its scale dependence are studied using the topography data from laser altimeter observations from recent lunar missions. As these two parameters are known, surface roughness (RMS slope) can be estimated by minimizing the difference between the observed and modeled radar echo strength. Surface roughness of several regions over Oceanus Procellarum and southeastern highlands on lunar nearside are studied, and preliminary results show that maira is smoother than highlands at 70 cm scale, whereas the situation turns opposite at 12 and 4 cm scale. Surface roughness of young craters is in general higher than that of maria and highlands, indicating large rock population produced during impacting process.